The nice thing about the ATV Hulu app is that you can log in to Hulu at a system level, and then individual channel apps can use that system-level login. If I wanted to watch+record, I'd watch live via the channel's app, and then watch the recording via Hulu. As you said, though, catching up to a live event was an awful UX.

FWIW, I've been trying PS Vue this month, and they handle that case far better than Hulu.